To develop a sophisticated understanding of algebraic representations, which is key to senior secondary success, our students need to appreciate the difference between a variable and an unknown, to have some sense of the meaning conveyed by expressions like 2x+4, and, more generally, to understand the answer to ‘why do we have to use letters instead of just numbers when doing mathematics?’ These ideas form with early experiences of algebra, which need to plant some of these seeds. This workshop will share an approach which focussing on the teaching of identities (starting with the distributive law of multiplication) rather than processes (“expand”, “factorise”), using video to see quantities varying, and variables as a sensible way to capture this variation. These videos can be followed by a sequence of re-enforcing activities, which will also be shared.

1. Variables vary (and constants are constant). Video is a powerful way to see variation, and algebraic/symbolic representations are powerful ways to describe and work with that variation.